dolphin/Source/Core/Common/Matrix.h

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// Copyright 2019 Dolphin Emulator Project
// SPDX-License-Identifier: GPL-2.0-or-later
#pragma once
#include <array>
#include <cmath>
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#include <functional>
#include <type_traits>
// Tiny matrix/vector library.
// Used for things like Free-Look in the gfx backend.
namespace Common
{
template <typename T>
union TVec3
{
constexpr TVec3() = default;
constexpr TVec3(T _x, T _y, T _z) : data{_x, _y, _z} {}
template <typename OtherT>
constexpr explicit TVec3(const TVec3<OtherT>& other) : TVec3(other.x, other.y, other.z)
{
}
constexpr TVec3 Cross(const TVec3& rhs) const
{
return {(y * rhs.z) - (rhs.y * z), (z * rhs.x) - (rhs.z * x), (x * rhs.y) - (rhs.x * y)};
}
constexpr T Dot(const TVec3& other) const { return x * other.x + y * other.y + z * other.z; }
constexpr T LengthSquared() const { return Dot(*this); }
T Length() const { return std::sqrt(LengthSquared()); }
TVec3 Normalized() const { return *this / Length(); }
constexpr TVec3& operator+=(const TVec3& rhs)
{
x += rhs.x;
y += rhs.y;
z += rhs.z;
return *this;
}
constexpr TVec3& operator-=(const TVec3& rhs)
{
x -= rhs.x;
y -= rhs.y;
z -= rhs.z;
return *this;
}
constexpr TVec3& operator*=(const TVec3& rhs)
{
x *= rhs.x;
y *= rhs.y;
z *= rhs.z;
return *this;
}
constexpr TVec3& operator/=(const TVec3& rhs)
{
x /= rhs.x;
y /= rhs.y;
z /= rhs.z;
return *this;
}
constexpr TVec3 operator-() const { return {-x, -y, -z}; }
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// Apply function to each element and return the result.
template <typename F>
auto Map(F&& f) const -> TVec3<decltype(f(T{}))>
{
return {f(x), f(y), f(z)};
}
template <typename F, typename T2>
auto Map(F&& f, const TVec3<T2>& t) const -> TVec3<decltype(f(T{}, t.x))>
{
return {f(x, t.x), f(y, t.y), f(z, t.z)};
}
template <typename F, typename T2>
auto Map(F&& f, T2 scalar) const -> TVec3<decltype(f(T{}, scalar))>
{
return {f(x, scalar), f(y, scalar), f(z, scalar)};
}
std::array<T, 3> data = {};
struct
{
T x;
T y;
T z;
};
};
template <typename T>
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TVec3<bool> operator<(const TVec3<T>& lhs, const TVec3<T>& rhs)
{
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return lhs.Map(std::less<T>{}, rhs);
}
constexpr TVec3<bool> operator!(const TVec3<bool>& vec)
{
return {!vec.x, !vec.y, !vec.z};
}
template <typename T>
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auto operator+(const TVec3<T>& lhs, const TVec3<T>& rhs) -> TVec3<decltype(lhs.x + rhs.x)>
{
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return lhs.Map(std::plus<decltype(lhs.x + rhs.x)>{}, rhs);
}
template <typename T>
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auto operator-(const TVec3<T>& lhs, const TVec3<T>& rhs) -> TVec3<decltype(lhs.x - rhs.x)>
{
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return lhs.Map(std::minus<decltype(lhs.x - rhs.x)>{}, rhs);
}
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template <typename T1, typename T2>
auto operator*(const TVec3<T1>& lhs, const TVec3<T2>& rhs) -> TVec3<decltype(lhs.x * rhs.x)>
{
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return lhs.Map(std::multiplies<decltype(lhs.x * rhs.x)>{}, rhs);
}
template <typename T>
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auto operator/(const TVec3<T>& lhs, const TVec3<T>& rhs) -> TVec3<decltype(lhs.x / rhs.x)>
{
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return lhs.Map(std::divides<decltype(lhs.x / rhs.x)>{}, rhs);
}
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template <typename T1, typename T2>
auto operator*(const TVec3<T1>& lhs, T2 scalar) -> TVec3<decltype(lhs.x * scalar)>
{
return lhs.Map(std::multiplies<decltype(lhs.x * scalar)>{}, scalar);
}
template <typename T1, typename T2>
auto operator/(const TVec3<T1>& lhs, T2 scalar) -> TVec3<decltype(lhs.x / scalar)>
{
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return lhs.Map(std::divides<decltype(lhs.x / scalar)>{}, scalar);
}
using Vec3 = TVec3<float>;
using DVec3 = TVec3<double>;
template <typename T>
union TVec4
{
constexpr TVec4() = default;
constexpr TVec4(TVec3<T> _vec, T _w) : TVec4{_vec.x, _vec.y, _vec.z, _w} {}
constexpr TVec4(T _x, T _y, T _z, T _w) : data{_x, _y, _z, _w} {}
constexpr T Dot(const TVec4& other) const
{
return x * other.x + y * other.y + z * other.z + w * other.w;
}
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constexpr TVec4& operator*=(const TVec4& rhs)
{
x *= rhs.x;
y *= rhs.y;
z *= rhs.z;
w *= rhs.w;
return *this;
}
constexpr TVec4& operator/=(const TVec4& rhs)
{
x /= rhs.x;
y /= rhs.y;
z /= rhs.z;
w /= rhs.w;
return *this;
}
constexpr TVec4& operator*=(T scalar) { return *this *= TVec4{scalar, scalar, scalar, scalar}; }
constexpr TVec4& operator/=(T scalar) { return *this /= TVec4{scalar, scalar, scalar, scalar}; }
std::array<T, 4> data = {};
struct
{
T x;
T y;
T z;
T w;
};
};
template <typename T>
constexpr TVec4<T> operator*(TVec4<T> lhs, std::common_type_t<T> scalar)
{
return lhs *= scalar;
}
template <typename T>
constexpr TVec4<T> operator/(TVec4<T> lhs, std::common_type_t<T> scalar)
{
return lhs /= scalar;
}
using Vec4 = TVec4<float>;
using DVec4 = TVec4<double>;
template <typename T>
union TVec2
{
constexpr TVec2() = default;
constexpr TVec2(T _x, T _y) : data{_x, _y} {}
template <typename OtherT>
constexpr explicit TVec2(const TVec2<OtherT>& other) : TVec2(other.x, other.y)
{
}
constexpr T Cross(const TVec2& rhs) const { return (x * rhs.y) - (y * rhs.x); }
constexpr T Dot(const TVec2& rhs) const { return (x * rhs.x) + (y * rhs.y); }
constexpr T LengthSquared() const { return Dot(*this); }
T Length() const { return std::sqrt(LengthSquared()); }
TVec2 Normalized() const { return *this / Length(); }
constexpr TVec2& operator+=(const TVec2& rhs)
{
x += rhs.x;
y += rhs.y;
return *this;
}
constexpr TVec2& operator-=(const TVec2& rhs)
{
x -= rhs.x;
y -= rhs.y;
return *this;
}
constexpr TVec2& operator*=(const TVec2& rhs)
{
x *= rhs.x;
y *= rhs.y;
return *this;
}
constexpr TVec2& operator/=(const TVec2& rhs)
{
x /= rhs.x;
y /= rhs.y;
return *this;
}
constexpr TVec2& operator*=(T scalar)
{
x *= scalar;
y *= scalar;
return *this;
}
constexpr TVec2& operator/=(T scalar)
{
x /= scalar;
y /= scalar;
return *this;
}
constexpr TVec2 operator-() const { return {-x, -y}; }
std::array<T, 2> data = {};
struct
{
T x;
T y;
};
};
template <typename T>
constexpr TVec2<bool> operator<(const TVec2<T>& lhs, const TVec2<T>& rhs)
{
return {lhs.x < rhs.x, lhs.y < rhs.y};
}
constexpr TVec2<bool> operator!(const TVec2<bool>& vec)
{
return {!vec.x, !vec.y};
}
template <typename T>
constexpr TVec2<T> operator+(TVec2<T> lhs, const TVec2<T>& rhs)
{
return lhs += rhs;
}
template <typename T>
constexpr TVec2<T> operator-(TVec2<T> lhs, const TVec2<T>& rhs)
{
return lhs -= rhs;
}
template <typename T>
constexpr TVec2<T> operator*(TVec2<T> lhs, const TVec2<T>& rhs)
{
return lhs *= rhs;
}
template <typename T>
constexpr TVec2<T> operator/(TVec2<T> lhs, const TVec2<T>& rhs)
{
return lhs /= rhs;
}
template <typename T, typename T2>
constexpr auto operator*(TVec2<T> lhs, T2 scalar)
{
return TVec2<decltype(lhs.x * scalar)>(lhs) *= scalar;
}
template <typename T, typename T2>
constexpr auto operator/(TVec2<T> lhs, T2 scalar)
{
return TVec2<decltype(lhs.x / scalar)>(lhs) /= scalar;
}
using Vec2 = TVec2<float>;
using DVec2 = TVec2<double>;
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class Matrix33;
class Quaternion
{
public:
static Quaternion Identity();
static Quaternion RotateX(float rad);
static Quaternion RotateY(float rad);
static Quaternion RotateZ(float rad);
// Returns a quaternion with rotations about each axis simulatenously (e.g processing gyroscope
// input)
static Quaternion RotateXYZ(const Vec3& rads);
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static Quaternion Rotate(float rad, const Vec3& axis);
Quaternion() = default;
Quaternion(float w, float x, float y, float z);
float Norm() const;
Quaternion Normalized() const;
Quaternion Conjugate() const;
Quaternion Inverted() const;
Quaternion& operator*=(const Quaternion& rhs);
Vec4 data;
};
Quaternion operator*(Quaternion lhs, const Quaternion& rhs);
Vec3 operator*(const Quaternion& lhs, const Vec3& rhs);
Vec3 FromQuaternionToEuler(const Quaternion& q);
class Matrix33
{
public:
static Matrix33 Identity();
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static Matrix33 FromQuaternion(const Quaternion&);
// Return a rotation matrix around the x,y,z axis
static Matrix33 RotateX(float rad);
static Matrix33 RotateY(float rad);
static Matrix33 RotateZ(float rad);
static Matrix33 Rotate(float rad, const Vec3& axis);
static Matrix33 Scale(const Vec3& vec);
// set result = a x b
static void Multiply(const Matrix33& a, const Matrix33& b, Matrix33* result);
static void Multiply(const Matrix33& a, const Vec3& vec, Vec3* result);
Matrix33 Inverted() const;
Matrix33& operator*=(const Matrix33& rhs)
{
Multiply(*this, rhs, this);
return *this;
}
// Note: Row-major storage order.
std::array<float, 9> data;
};
inline Matrix33 operator*(Matrix33 lhs, const Matrix33& rhs)
{
return lhs *= rhs;
}
inline Vec3 operator*(const Matrix33& lhs, Vec3 rhs)
{
Matrix33::Multiply(lhs, rhs, &rhs);
return rhs;
}
class Matrix44
{
public:
static Matrix44 Identity();
static Matrix44 FromMatrix33(const Matrix33& m33);
static Matrix44 FromQuaternion(const Quaternion& q);
static Matrix44 FromArray(const std::array<float, 16>& arr);
static Matrix44 Translate(const Vec3& vec);
static Matrix44 Shear(const float a, const float b = 0);
static Matrix44 Perspective(float fov_y, float aspect_ratio, float z_near, float z_far);
static void Multiply(const Matrix44& a, const Matrix44& b, Matrix44* result);
static void Multiply(const Matrix44& a, const Vec4& vec, Vec4* result);
// For when a vec4 isn't needed a multiplication function that takes a Vec3 and w:
Vec3 Transform(const Vec3& point, float w) const;
Matrix44& operator*=(const Matrix44& rhs)
{
Multiply(*this, rhs, this);
return *this;
}
// Note: Row-major storage order.
std::array<float, 16> data;
};
inline Matrix44 operator*(Matrix44 lhs, const Matrix44& rhs)
{
return lhs *= rhs;
}
inline Vec4 operator*(const Matrix44& lhs, Vec4 rhs)
{
Matrix44::Multiply(lhs, rhs, &rhs);
return rhs;
}
} // namespace Common